This book focuses on percolation on high-dimensional lattices. We give a general
introduction to percolation, stating the main results and defining the central objects. We …

The model of random interlacements was introduced in 2007 by A.-S. Sznitman in the
seminal paper [41], motivated by questions about the disconnection of discrete cylinders and …

We consider continuous time interlacements on ℂ d, d≥ 3, and investigate the scaling limit
of their occupation times. In a suitable regime, referred to as the constant intensity regime …

We provide an explicit algorithm for sampling a uniform simple connected random graph
with a given degree sequence. By products of this central result include:(1) continuum …

We consider ℤ d, d≥ 3. We investigate the vacant set Vu of random interlacements in the
strongly percolative regime, the vacant set V of the simple random walk and the excursion …

In this article we obtain uniform estimates on the absorption of Brownian motion by porous
interfaces surrounding a compact set. An important ingredient is the construction of certain …

The main focus of this article concerns the strongly percolative regime of the vacant set of
random interlacements on Z d, d≥ 3. We investigate the occurrence in a large box of an …

We consider random interlacements on ℤ d, d≥ 3, when their vacant set is in a strongly
percolative regime. Given a large box centered at the origin, we establish an asymptotic …

We define the model of two-dimensional random interlacements using simple random walk
trajectories conditioned on never hitting the origin, and then obtain some properties of this …

We extend the Aldous–Broder algorithm to generate the wired uniform spanning forests
(WUSFs) of infinite, transient graphs. We do this by replacing the simple random walk in the …